The city’s ordinance had been scheduled to take effect last June, but was blocked by court order after a lawsuit by CTIA-The Wireless Association, which said it violated freedom of speech. In September, U.S. District Judge Edward Chen of San Francisco issued an injunction against the entire ordinance because it contained a disputed warning that “this potential risk is greater for children.”

But the City Council then removed that warning, and on Wednesday Chen allowed the rest of the ordinance to take effect, rejecting the industry group’s request for a stay while it asks a federal appeals court to declare the entire ordinance unconstitutional.

The measure requires retailers to notify customers that the federal government sets radiation standards for cell phones, and that a user may be exposed to levels that exceed those standards by carrying a phone in a pocket or tucked into a bra when the device is connected to a wireless network.

Chen ruled in September, and reiterated Wednesday, that Berkeley had based that warning on the Federal Communications Commission’s research and guidelines. By contrast, he said, the now-discarded warning about a potentially greater risk for children was not based on scientific consensus or federal guidelines, but was a matter of scientific debate that retailers could not be required to pass on to customers.

In arguing that the overall ordinance was unconstitutional and seeking a stay, CTIA cited a 1985 U.S. Supreme Court ruling that said government agencies could require product-sellers to pass along government messages only if the statements were “factual and uncontroversial.” The industry group contended Berkeley’s message was overstated and misleading, since the FCC, by its own admission, built in a considerable safety margin when it set guidelines for carrying cell phones.

But Chen said the city had referred accurately to the FCC guidelines and would not interfere with legitimate free-speech rights by requiring the standards to be communicated to customers.

Although the federal agency established standards that may have been stricter than necessary, “it did set specific limits and did so in order to assure safety,” Chen said.

CTIA’s disagreement is not enough to make the city’s message “controversial,” the judge said, noting that “science is almost always debatable at some level.” He also said the industry group and its members remain free to criticize the message, as long as they comply with the requirement to pass it along to customers.